Don't look at it from a caliber perspective - if 300m is a goal, then what cartridge will deliver 1,000 foot pounds of force, the ethical limit, that far? Not anything you can shoot effectively from a 10" barrel. It's a simple ballistics exercise.
For that matter shooting deer at 300 is problematic regardless of cartridge. I started out with that in mind, years ago, with .308, then moved to .30-06, tried .30-30, 6.8SPC - and then sat down to really think it thru.
I had been hunting one particular section of public ground for 40 years, and on one of those rarer mornings while still awake I plotted every known kill I had knowledge of where I knew the location of both shooter and game. Most were shots under 80m. That coincided with verbal testimony of the shooters, too, and also corroborated what I had seen elsewhere or in other tales of legendary hunting prowess. The bulk of the shots aren't long distance, they are actually 25-80m.
First, because the hunters put themselves in that range where deer traveled. Second, they simply couldn't see any further due to cover. Deer in rut tend to hold close to cover during the season.
I then checked to see how far 5.56 would hold at least 1,000 foot pounds of force and 80m is the limit. It is extended for larger bullets, of course, but most won't carry 1,000 foot pounds past 125m from a ten inch barrel. They don't start high enough to keep the energy - and the larger bullets also drop sooner. You do get more power and an incremental extension of range but 300 is too far for ethical hunting purposes, IF you could even get the shot.
I built an AR in 5.56 for close in hunting and use 70 gr OTM for ammo. If shots longer than that were part of the plan, then 6.8, .30-30, or .30-06 would be the better choice - I sold off the .308's long ago as cheap surplus dried up in the '90s. 5.56 hasn't, tho, and I picked up boxes of Tula just the other day retail at 5.99.
I will never find 6.8 or .300BO at those prices, and the marginal difference in range hunting deer will be a small incremental change - one that only extends a shot into even deeper cover where I can't see any movement anyway without a scope. That means 2-4 power on top of what I built as an iron sights HD gun which inside a home will primarily use a 25 foot lighted point for aiming.
It becomes an exercise in contradictory purposes trying to build a 300m deer gun that serves as an SBR for HD. Especially since the ballistics just aren't there.
Considering the bullet drip of .300BO at 300m, I wouldn't consider it at all and choose something flatter shooting anyway. Again, it's not about one vs another, it's about defining your range and target then choosing a cartridge that actually fits. Given a ten inch barrel - nothing will do that job effectively. It's not what an SBR does, at all.
80-100m is the practical and ethical limit for an AR with 10" barrel - and just about any cartridge you pick will do that. I picked 5.56 because it saved me $300 buying another upper and that money can go to ammo or accessories. Plus - I will likely not ever Kaboom the 5.56 because a stray .300BO got in a magazine.